Theorem 2.3 ([1]}, [2]}) 
Let \((M,\omega )\)  be a symplectic surface, and \(F\colon M\rightarrow {\mathbb {R}}\)  be a simple Morse function. Let \(O\in M\setminus \partial M\)  be a critical point for the function \(F.\)  Then there exists a coordinate chart \((p,q)\)  centered at \(O\)  such that \(\omega =dp\wedge dq\)  and \(F=\lambda \circ S\)  where \(S=pq\)  or \(S=p^2+q^2.\)  Here \(\lambda \)  is a smooth function of one variable defined in some neighborhood of the origin \(0\in {\mathbb {R}}\)  and \(\lambda ^{\prime }(0) \ne 0.\) 
Moreover:
